(1−√(5))×(2−√(5)) (1 + 4 √(10) )(2 - √(10) )

Question

(1−√(5))×(2−√(5))

`(1 + 4 √(10) )(2 - √(10) )`

Answer 1

To simplify these expressions, you can either use a calculator (which I'm assuming your teacher doesn't want you to do) or FOIL (distribute).

The first one would be:


`(1- √(5)) (2- √(5)) \\ewline =(1)(2)+(1)(- √(5) )+(- √(5))(2)+(- √(5))(- √(5)) \\ewline =2- √(5)-2 √(5)+5 \\ewline =7-3 √(5)`

The second one would be:


`(1+4 √(10))( 2- √(10)) \\ewline =(1)(2)+(1)(- √(10))+(4 √(10) )(2) +(4 √(10))(- √(10)) \\ewline =2-√(10)+8 √(10) -40 \\ewline =-38+7 √(10)`